SOLUTION: Express the function f(x)=log_(3)(9^(6 x+4) 81^(6 x+ 8)) without logarithms.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Express the function f(x)=log_(3)(9^(6 x+4) 81^(6 x+ 8)) without logarithms.      Log On


   

Question 418142: Express the function
f(x)=log_(3)(9^(6 x+4) 81^(6 x+ 8))
without logarithms.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Express the function
f(x)=log_(3)(9^(6 x+4) 81^(6 x+ 8))
without logarithms.
..
f(x)=log(3*9^(6x+4)*81^(6x+8))
change to base 3
=log(3*(3^2)^(6x+4)*3^4^(6x+8))
multiply exponents
=log(3*(3)^12x+8*(3)^(24x+32))
add exponents
=log(3*(3^(36x+40))
=log(3^(36x+41))
use exponent rule for logarithms
=(36x+41)*log3
use calculator for log 3
=(36x+41)*.477
ans:
f(x)=17.18x+19.56